A brief note of explanation concerning the origin of this book might prove of interest to the reader. Initially, it was envisaged as one volume in a series dealing with various aspects of physical processes in the chemical industry and it was intended that it should cover the mathematical techniques applied in the companion volumes. During the course of writing, however, it became increasingly evident that the contents could, with little modification, be of interest to a considerably wider readership than that for which the series was intended. It was therefore decided to publish the work in its own right.

The aim of the authors throughout has been to produce a text of wide range from which the student could derive the maximum benefit with the minimum of assistance from other sources. With this aim in view, the book starts with a revision course in basic algebra, geometry, and trigonometry, and subsequent chapters range over a wide field of mathematical techniques and their applications. Although the chapters are arranged in logical sequence, many are virtually self-contained and may be read in isolation. It is hoped that the inclusion of a large number of worked examples will materially assist the reader who is attempting to teach himself.

2. REVIEW OF ELEMENTARY PLANE TRIGONOMETRY - The Circular Functions; Radian Measure; Simple Applications of Trigonometry; Solution of General Triangles; Circular Functions of the Sum and Difference of Two Angles; Solution of Trigonometric Equations; The Inverse Circular Functions -

3. CO-ORDINATE PLANE GEOMETRY OF THE STRAIGHT LINE - Cartesian and Polar Co-ordinates; Loci; Various Forms of the Equation of a Line; Distance from a Point to a Line; Angle between Two Lines; Point of Intersection of Two Lines; Pairs of Lines; Problems Involving Straight Lines -

4. CO-ORDINATE PLANE GEOMETRY OF THE CIRCLE -Equations of a Circle; Equation of the Tangent to a Circle; Equation of the Normal to a Circle; Length of the Tangent from a Point to a Circle; Intersection of a Circle with a Line; Intersection of Two Circles; Problems Involving Circles and Lines -

5. THE BINOMIAL EXPANSION -Permutations and Combinations; The Binomial Expansion for Positive Integral Index; Some Properties of the Binomial Coefficients; The Binomial Expansion for any Index; Validity of the Binomial Expansion for any Index; Applications of the Binomial Expansion -

7. FUNCTIONS AND LIMITS - Functional Relationships; Geometrical Representation of a FunctionalRelationship; Values and Limits of a Function; The Derivative of a Function -

8. DIFFERENTIATION - Differentiation from First Principles; Differentiation of x"-Differentiation of sin x and cos x; Differentiation of Sums, Differences, Products, and Quotients; Differentiation of Compound Circular Functions; Differentiation of a Function of a Function-Differentiation of log x; The Exponential and Hyperbolic Functions; Differentiationof Inverse Circular and Inverse Hyperbolic Functions -

9. APPLICATIONS OF DIFFERENTIATION - Tangents and Normals to Curves; Estimation of Small Errors; Maclaurin and Taylor Series; Newton's Method for the Approximate Solution of Equations; Maxima and Minima -

10. INTEGRATION - Integration as the Inverse of Differentiation; Special Methods of Integration; Integration Using Partial Fractions; Integration by Substitution; Integration by Parts; The Definite Integral; Reduction Formulae -

12. COMPLEX NUMBERS - General Solution of the Quadratic Equation; The Argand Diagram; Addition,Subtraction, Multiplication, and Division of Complex Numbers-The Polar Form of the Complex Number; Multiplication and Division in Polar Form; Powers and Roots of Complex Numbers; Functions of the Complex Variable -

20. CONTROL CHARTS - Control Charts for Number Defective; Standard Error of the Average; Control Limits; Control Charts for Average and Range -

21. POPULATION AND SAMPLE - The Sample Used to Predict the Population; Degrees of Freedom Distributionof Averages; Confidence Limits; Single-sided and Double-sided Confidence Limits; Distribution of the Ratio of Two Variance Estimates -